The Lattice QFT Group Dr. Andreas Jttner Prof. Chris Sachrajda Who - - PowerPoint PPT Presentation

The Lattice QFT Group

• Prof. Jonathan Flynn
• Dr. Andreas Jüttner
• Prof. Chris Sachrajda

Who Is Who

Staff: Jonathan Flynn Andreas Jüttner Chris Sachrajda Postdoc: Nils Asmussen Masanori Hanada Postgrads: Ryan Hill Ben Kitching-Morley James Richings

Motivation

• Standard Model - Electroweak and

Strong interaction consistently described in terms of renormalisable
 Quantum Field Theory

• It works incredibly well
• But there is evidence that it’s not the


whole story: 
 dark matter, dark energy, 
 matter-anti-matter asymmetry, … 
 indicate that there must be sth. else

• So far no smoking gun

Motivation

• SM tests / search for new physics

• Direct: new particles in spectra


• Indirect: SM provides correlations 


between processes experiment + theory 
 to over constrain SM → precision physics

• Hadronic uncertainties very often dominating error budget
• Lattice QCD is the tool of choice to compute hadronic matrix


elements and is becoming increasingly precise in its predictions


SM coupling constants

SM-sector typical coupling mediator WEAK 10-5GeV-2 Z, W± EM 1/137 γ QCD 0-O(1) gluons

PDG

non-perturbative physics - proton mass and hadron decays

Illustrations from slides by Laurent Lellouch

Proton Neutron

non-perturbative physics - proton mass and hadron decays

π ?

QCD
 EM WEAK

π

QCD
 EM WEAK

hadronic decay

meson

Decays l ν ?

QCD
 EM WEAK EM WEAK

leptonic decay

meson

experimental and theoretical study of decays furthers understanding

• f Standard Model’s flavour sector

Lattice QCD

• Lagrangian of massless gluons and almost massless quarks
• What experiment sees are bound states, e.g. mπ,mP ≫ mu,d
• Underlying physics non-perturbative

Free parameters:

• gauge coupling g → αs=g2/4π
• quark masses mf = u,d,s,c,b,t

LQCD = −1 4F a

µνF a µν +

X

f

¯ ψf (iγµDµ − mf) ψf finite volume, space-time grid (IR and UV regulators)

∝ a−1 ∝ L−1 → Well defined, finite dimensional Euclidean path integral → From first principles, solve via MCMC

8

Path integral quantisation: h0|O|0i =

1 Z

R D[U, ψ, ¯ ψ]Oe−iSlat[U,ψ, ¯

ψ]

h0|O|0i =

1 Z

R D[U, ψ, ¯ ψ]Oe− Slat[U,ψ, ¯

ψ]

Euclidean space-time
 Boltzmann factor

Lattice QCD

• Evaluate discretised path integral in finite volume by means of Monte Carlo


simulation

• even on the most powerful high-performance computers a set of simulation


can easily take months if not years

State of the art of lattice QCD simulations

What we can do

• simulations of QCD with dynamical (sea) 


u,d,s,c quarks with masses
 as found in nature

• bottom only as valence quark
• cut-off
• volume

Nf = 2, 2 + 1, 2 + 1 + 1

a−1 ≤ 4GeV L ≤ 6fm

action density of RBC/UKQCD physical point DWF ensemble

Parameter tuning start from educated guesses and compute

• tune light quark mass aml such that

• tune strange quark mass such that 

• determine physical lattice spacing

amπ amP = mP DG

π

mP DG

P

amπ amK = mP DG

π

mP DG

K

a = afπ f P DG

π

IMPORTANT:


• nce the QCD-parameters 


are tuned no further parameters need to be fixed 
 and we can make fully predictive simulations of QCD

works well for some quantities - 
 e.g. spectrum from LQCD vs. experiment

BMW Science 322 (2008) 1224

Lattice QFT — wide range of skills

Computing

• exascale computing
• using hardware efficiently
• data analysis
• developing purpose built hardware

Quantum Field Theory

• many fundamental questions open:


peculiarities of Euclidean Field Theory — understand how 
 to ask the question (QED+QED, renormalisation, finite volume effects, finite density, phase diagram of QCD, …) Algorithms

• development of new simulation algorithms


use physics intuition/knowledge of dynamics

• address fundamental questions:
• critical slowing down
• renormalisability of algorithms

Some of the questions we are addressing:

Are there any other particles out there?

CP

Why is there something rather than nothing? How to make sense out of LHCb data? Are cosmology and particle 
 physics intimately related?

Any other particles out there?

Example - the muon g-2 There is a persistent 2.5-3.5σ tension between experiment and theory and there are many potential BSM candidates that could explain the discrepancy

PDG

contribution value error QED (4-loop, LO 5-loops) 11658471.895 0.2 Weak incl. 2-loops 15.4 1.8 QCD leading VP 692.3 4.2 QCD light-by-light 10.5 2.6 SM TOTAL 11659181.5 4.9 Experiment 11659209.1 6.3

non-perturbative 
 contributions q q q Fermilab 1.6 J-PARC 4.3 (later ~1) An ab initio prediction of the hadronic contributions is still missing

Any other particles out there?

q q We are computing the leading order contribution The aim is to provide the first real SM prediction, match current
 experiment-based prediction and go beyond Computing it in Lattice QCD is basically understood The current challenge is to include QED and strong isospin breaking corrections There are many conceptual issues in QFT which we have to deal with in parallel with understanding how to do the computation itself

Why is there something rather than nothing?

Sakharov 1967:

• C and CP violation
• baryon number violation
• thermal inequilibrium

CP violation needed to explain why there is matter in the universe assuming symmetric beginning SM does not provide sufficient CP violation to account for observed amount of matter s d Precision physics study of SM CP violation in search of new physics CP violation in Kaons: direct and indirect CP violation both observed and measured experimentally (after decades of efforts) very sensitive to New Physics

Why is there something rather than nothing?

Direct CP-violation: predictions of decay amplitudes K→ππ “This is by far the most 
 complicated project that
 I have ever been 
 involved with.”

(ε/ε)exp

Gino Isidori at Kaon 2016, Birmingham

ηij = A(KL → πiπj) A(KS → πiπj)

(ε/ε)exp Lattice QCD studies of K → ππ could be awarded a Nobel Prize !

KL mainly CP odd, 3π CP odd
 KS mainly CP even, 2π CP even weak 
 eigenstates

Why is there something rather than nothing?

Indirect CP violation — KL-KS Mass difference:


• experimentally ΔMK=3.483(6)⨉10-12MeV (PDG)

• suppressed by 14 orders of magnitude with respect to QCD → poses strong

BSM constraints (e.g. (1/Λ)2 BSM contribution) knowing 
 ΔMK at 10%-level → Λ≥104TeV


• SD about 70% of experimental value - rest LD?

¯ sd¯ sd

We are computing the mass difference from first principles — the results could have tremendous impact on searches for new physics K K

How to make sense out of LHCb data?

First observed by LHCb, CMS

Quark Flavour Physics

e.g tree level leptonic B decay: Experimental measurement + theory prediction allows for 
 extraction of CKM MEs

Γexp.

???

= VCKM(WEAK)(EM)(STRONG)

Assumed factorisation:

experiment theory prediction

• utput

{

{

{

Γ(B → lνl) = |Vub|2 mB 8π G2

F m2 l

✓ 1 − m2

l

m2

B

◆2 f 2

B

20

Cosmology ↔ Particle Physics

CMB provides a unique view on the very early
 (Planck-Scale) Universe where quantum gravity becomes relevant d-1 QFT(no gravity) is holographic dual of QG Idea: study 3d QFT and use holography to make 
 predictions for QG

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Perturbatively this has shown successful but PT breaks down → lattice simulations

Simulations of lattice quantum field theory

Nice interplay between:

• Quantum field theory
• Algorithms
• Hardware/computing

Not only QCD - lattice quantum field theory also in:

• SUSY
• Quantum gravity
• Model-studies
• Other dimensions
• Composite Higgs
• …


Study variations of QCD

• What would QCD look like with 


quark masses other than the ones 
 found in nature?
 (different gauge group, different 
 #/representation of fermions)

• The QCD phase diagram can be 


studied

Links/Conferences

Close links with:

• Maths in Soton
• University of Edinburgh
• Columbia University New York, US
• Brookhaven National Lab, US
• CP3-Origins, Denmark
• KEK Tsukuba, Japan
• Rome, Italy

Postgrad student visits in last two years:

• KEK Japan
• BNL US
• Columbia University US

Conference visits:

• Annual Lattice Conference:


UK, Japan, US, Germany, Australia, US, Italy, China, …

• topical workshops around the world

Alumni

Vera Gülpers postdoc in Edinburgh Antonin Portelli Lecturer Edinburgh Francesco Sanfilippo Staff Rome Marina Marinkovic postdoc Dublin Andrew Lytle postdoc Glasgow Andreas Jüttner Lecturer Southampton Laurent Lellouch Professor Marseille Hartmut Wittg Professor Mainz Luigi Del Debbio Professor Edinburgh

Soton Postdocs:

James Harrison Flowminder Edwin Lizarazo Perpetuum Tobias Tsang postdoc Edinburgh Matt Spraggs ASV Ben Samways Ericsson Elaine Goode Actica Tadeusz Janowski

postdoc CP3-Origins, now Edinburgh

Tom Rae

post doc Mainz, Wuppertal, now teacher

Chris Dawson Google Andrew Lawson FiveAI

Soton Postgrads:

Many other physics topics — ask us…

literature